In order for an organization to effectively manage risk at an enterprise-wide level, a risk management system that can apply methodologies able to integrate the various risks faced by the organization should be used. To be most effective, the system must be capable of integrating risks spanning multiple business units and geographical locations.
As risk measures and their underlying models grow more complex, many risk managers are relying more on scenario-based methods. In these methods, future uncertainty is represented in terms of a set of scenarios, where each scenario represents a possible future economic situation. Accordingly, a scenario set consists of one or more scenarios, and is often interpreted as a set of possible future situations.
Mark-to-Future™ (MtF) is an example of a scenario-based approach that measures and manages a variety of risks. An example of an implementation of this methodology and why it represents a standard for simulation-based risk management can be found in pending U.S. patent application Ser. No. 09/811,684, the contents of which are herein incorporated by reference. MtF provides flexibility in the definition of scenarios of interest, sets of financial instruments, portfolio hierarchies, and risk measures. The elements must be defined in a coordinated manner to ensure a sensible result.
Consider, for example, using MtF to estimate the Value-at-Risk (VaR), based on historical data, of a large, diverse, portfolio. Given the instruments in the portfolio and their respective pricing models, it is first necessary to identify a set of underlying risk factors for the portfolio. A risk factor is any observable economic variable whose value, or change in value, may be translated into a change in the value of a portfolio under consideration. The set of all risk factors and their values determines a “state of the world” and provides an economic snapshot under which the portfolio under consideration may be evaluated during a simulation. These risk factors might include, for example, interest rates, foreign exchange rates, commodity prices, equity prices, market indices, credit spread curves, implied volatilities, and macroeconomic factors.
Once historical time series data for all risk factors have been obtained, the data can be manipulated to produce a consistent set of scenarios. A scenario set is a list of risk factors and their values at one or more points in the future that completely define an economic situation. These scenarios, once produced, act as input to the pricing models, which calculate scenario-dependent prices for all instruments. By combining the resulting prices with the number of units of a particular instrument held in a portfolio or alternatively the “portfolio position information”, a profit-and-loss distribution for the portfolio can be obtained, from which the VaR can be estimated.
Scenarios are the basis of risk measurement in MtF. The more precisely the scenarios span the set of possible future events, the more accurate the risk measures calculated from the scenarios will be. The ability to obtain more accurate risk measures allows for more effective risk management.
Since many risk measures (e.g. VaR) are of a statistical nature, generating statistical scenarios is an important part of MtF, or any other simulation-based methodology. Statistical scenarios are created by assuming that risk factors behave according to specific models, and then these models are used to generate possible future outcomes. The models may range, for example, from simple historical approaches, which assume that previous risk factor changes recur in the future, to complex jump diffusion processes. A common feature is that a large number of scenarios are created and assumed to represent the set of all possible future events.
Statistical or model-based scenarios are only as good as the models used. Often the models are too simple to capture the complex interactions of global financial markets. Therefore, risk management practitioners use in addition, non-statistical scenarios such as “worst-case scenarios”, “stress scenarios”, and “sensitivity scenarios” to account for some of the deficiencies of model-based statistical scenarios. Accordingly, there is a need for a system for creating and handling different types of scenarios, including both statistical scenarios and non-statistical scenarios.
Risk management has progressed from measuring market, credit, liquidity and other risks in isolation, to measuring them jointly, and taking into account correlation and diversification effects. Proper joint measures require the definition of scenarios covering the set of all risk factors, and complete descriptions of the relationships among risk factors. In this way, a consistent view of the future can be produced, leading to consistent measurement of different types of risk.
Although the task of defining scenarios in this manner may appear to be simple (i.e. take all of the risk factors, estimate their inter-relationships and generate scenarios), practical problems typically arise.
Consider the joint measurement of market and credit risk, for example. The set of risk factors typically number in the thousands, while the number of counterparties often reaches the tens of thousands. As a result, the combined set of risk factors can quickly become unmanageable. Furthermore, the essential properties of the risk factors, such as historical trends, reporting frequencies and future expectations, may also differ substantially. Accurately representing the evolution of risk factors may therefore involve a wide range of statistical methods.
A large number of risk factors with different properties complicates the task of generating statistical scenarios. The dynamic nature of scenario generation processes presents a further challenge, namely, the system that produces scenarios needs to be flexible and extensible. As risk management expands in scope, new risk factors are continually introduced. Adding these risk factors to existing scenarios can be difficult, and often requires changes throughout the scenario generation process. For example, adding a new risk factor that is non-normally distributed to a set that is normal requires not only a new model, but also the definition of how this risk factor interacts with every existing risk factor. This cannot be handled by simply adding to an existing variance-covariance matrix or even re-calculating the matrix; the addition of a new codependent structure is typically required.
Furthermore, new models for generating scenarios appear in the risk management and finance literature frequently. Some are extensive, dealing jointly with a variety of risk factors, while others focus on marginal distributions of a single risk factor. Ideally, when a new marginal model (i.e. a model that focus on marginal distributions of a single risk factor) can be applied to a particular type of risk factor, it should be possible to simply substitute it for the existing model without affecting other risk factors included in the scenarios. However, scenario-based risk management systems that exist in the prior art are generally not equipped with this capability. Similarly, if a new joint model (i.e. a model that deal jointly with a variety of risk factors) is proposed in the literature, it is more convenient to reuse as much of an existing model and its implementation as possible than to undertake major changes to the existing scenario generation process for risk management.
It is important that the nature of a scenario set can be communicated to different audiences (e.g. senior management, a Board of Directors, auditors, traders, or other risk management personnel). However, while senior management may prefer a very high-level, non-technical description, in contrast, those who implement and maintain the scenario set need a thorough understanding of all technical details. For example, the phrase “a multi-step Monte Carlo scenario set in which the interest rates mean revert and the equities grow, over time” may sufficiently describe a scenario set for managerial purposes. In contrast, the actual generation of this scenario set may require a more detailed specification, for example: “a multi-step quasi Monte Carlo method using an equally weighted variance-covariance (VCV) matrix for Canadian, American and Australian interest rates where each curve is represented by three components that mean revert, and American equities, adjusted for stock splits that grow over time.”
The second description above indicates, to some extent, the complexity of the models and risk factor relationships that typically underlie statistical scenarios. Explaining or understanding statistical scenario generation at a detailed level is often difficult for two main reasons. First, the models for individual risk factors and their joint behaviour are typically combined into one single, large model, making it hard to isolate their respective properties. Second, the calibration of this model is usually done in one long and involved process.
Accordingly, there is a need for a generic, structured framework for generating scenarios consistently, and that allows for scenario sets to be communicated to a number of different audiences in a simplified way.